In the actual process of manufacturing aluminum products in an aluminum plant, cylindrical aluminum ingots are processed on an extruding machine. This extruding machine is in fact a batch processing machine, serving to process jobs one after another in each batch. Considering the actual production situation, there is a necessary period of setup time varying over time when processing each batch of aluminum ingots. In addition, the production efficiency will be improved continuously over time, i.e., the actual processing time of an aluminum ingot depends on the positions thereof or a sequential position of the batch holding the aluminum ingot. That is to say, if an aluminum ingot is processed later, it will take less time to complete the extrusion of the aluminum ingot. It thus can be seen that the processing time of an aluminum ingot can be expressed as a decreasing function related to its position. In this production scenario, the configurations of a single machine and parallel machines have different production requirements. Therefore, the scheduling system provides corresponding solving strategies for actual production scheduling circumstances in two cases of a single machine and parallel machines. The variable neighborhood search (VNS) algorithm was put forward by Mladenovic and Hansen in 1997, while the gravitational algorithm, also an efficient optimization algorithm, was initially put forward in 2009. In recent years, many scholars have made extensive studies on such algorithms and applied them in many practical combinatorial optimization problems.
However, during the process of invention-creation, the inventor has found that the prior art has some disadvantages as follows: (1) with regard to study, in one aspect, studies were reported in previous documents with consideration of fixed processing time. In actual conditions, the actual processing time of a job and the setup time of a batch are usually related to the position of the job and the starting setup time of the batch due to the deterioration and learning effect of a machine. In another aspect, it is rarely found that a document and a method have involved a parallel machine processing system with deterioration and learning considerations, especially with maximum lead time as the optimization objective, and this problem may decide the production efficiency and service quality of an enterprise in some actual applications. (2) With regard to study method, factors influencing the performance of the VNS algorithm mainly include the quality of an initial solution, a neighborhood structure, and a search strategy in the neighborhood structure. In some cases, the limitations of the initial solution and the neighborhood structure may cause the VNS algorithm to plunge into local optimum early, and consequently, it is impossible to obtain a good scheduling scheme.